What is the integral of 2/(3\sqrt[4]{x^3)} ?

The integral of 2/(3\sqrt[4]{x^3)} is 8/3 \sqrt[4]{x}+C

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integral of 2/(3\sqrt[4]{x^3)}

\int \frac{2}{3 4 x ^{3}} d x

\frac{8}{3} 4 x + C

Solution steps

\int \frac{2}{3 4 x ^{3}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{3} \cdot \int \frac{1}{4 x ^{3}} d x

4 x^{3} = x^{\frac{3}{4}},

assuming

x \geq 0

= \frac{2}{3} \cdot \int \frac{1}{x ^{\frac{3}{4}}} d x

Apply the Power Rule

: 4 x^{\frac{1}{4}}

= \frac{2}{3} \cdot 4 x^{\frac{1}{4}}

Simplify

\frac{2}{3} \cdot 4 x^{\frac{1}{4}} : \frac{8}{3} 4 x

= \frac{8}{3} 4 x

Add a constant to the solution

= \frac{8}{3} 4 x + C

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What is the integral of 2/(3\sqrt[4]{x^3)} ?
The integral of 2/(3\sqrt[4]{x^3)} is 8/3 \sqrt[4]{x}+C